Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  scanf("%d", &n);
  int i = 1;
  int b = 1;
  bool ok = false;
  while (b <= n) {
    int a = n - b;
    double dsqrt = sqrt(1 + 8.0 * a);
    int idsqrt = dsqrt;
    if (dsqrt == idsqrt && idsqrt != 1 && (idsqrt - 1) % 2 == 0) {
      printf("YES\n");
      ok = true;
      break;
    }
    i++;
    b = (i * (i + 1)) / 2;
  }
  if (!ok) printf("NO\n");
  return 0;
}